Two families went to the event. The first family bought two children's tickets and one adult ticket and paid a total of 8.2 euros. The other family bought three children's tickets and two adult tickets and paid a total of 14.1 euros. Can you tell me how much one child costs and how much one adult ticket costs?

Step-by-step explanation:

step a system of two equations         c = child ticket     a = adult ticket

eq 1)  2c + 1a = 8.2            multiply by 2

eq 2) 3c + 2a = 14.1

I will multiply eq 1 times TWO and subtract eq 2 from eq 1a)

         eq 1a)  4c + 2a = 16.4

          eq 2)  3c + 2a = 14.1

subtract  (4c - 3c) + (2a -2a)  = 16.4 - 14.1  

                    c      +       0       =   2.3 euros     for one child ticket

Now find the adult ticket price,  plug 2.3 for c into eq 1)

     eq 1)  2c + 1a = 8.2

     eq 1)  2(2.3) + 1a = 8.2         solve for a

                 4.6  + a   =  8.2         substract 4.6 from both sides

                             a =  8.2 - 4.6

                               =   3.6 euros    for one adult ticket

double check using eq 2)    we know c and a values

    eq 2)  3c + 2a = 14.1

    eq 2)  3(2.3) + 2(3.6) = 14.1

                   6.9 + 7.2    =  14.1

                          14.1    =  14.1

rick would give her the best deal as he will charge $8.88 per hour

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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